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The Graded Unfolding Model: A Unidimensional Item Response Model for Unfolding Graded Responses

Roberts, James S.; Laughlin, James E
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Attitude Measures, Item Response Models, Unfolding Technique, Unidimensionality (Tests)


Binary or graded disagree-agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate. Advances in item response theory (IRT) have led to the development of several parametric unfolding models for binary data, but IRT models for unfolding graded responses have not been addressed in the psychometric literature. A parametric IRT model for unfolding either binary or graded responses was developed in this study. The model, called the graded unfolding model (GUM), is a generalization of Andrich & Luo's (1993) hyperbolic cosine model for binary data. A joint maximum likelihood procedure was implemented to estimated GUM parameters, and a subsequent recovery simulation showed that reasonably accurate estimates could be obtained with minimal data demands (e.g., as few as 100 subjects and 15 to 20 6-category items). The applicability of the GUM to common attitude testing situations was illustrated with real data on student attitudes toward capital punishment. (68pp.)

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